%
% epage 241
% 
% lawpop
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; 
clc; 

addpath('../../Code/CSTool');
load lawpop;      % <- the total population 

% get a random sample from the total population of 15:
rand('seed',0); 
ns   = 15; 
inds = unidrnd(size(lawpop,1),1,ns);
law  = lawpop(inds,:); 

% get the population variances: 
pop_var_lsat = var(lawpop(:,1)); 
pop_var_gpa  = var(lawpop(:,2)); 

% estimate the population variance: 
sam_var_lsat = var(law(:,1));
sam_var_gpa  = var(law(:,2)); 

% get the bootstrapped estimate of the standard error of the variance
% 
B = 4000; 

% (of the lsat score): 
bootstat = bootstrp( B, @var, law(:,1) );  
fprintf('the population variance and sample variance is = (%10.5f,%10.5f)\n',pop_var_lsat,sam_var_lsat); 
fprintf('the bootstraped estimate of the SE of the variance of lsat is %10.5f\n', std( bootstat ) ); 
fprintf('the bootstraped estimate of the bias in the variance of lsat is %10.5f\n', mean( bootstat )-sam_var_lsat );

% (of the gpa): 
bootstat = bootstrp( B, @var, law(:,2) ); 
fprintf('the population variance and sample variance is = (%10.5f,%10.5f)\n',pop_var_gpa,sam_var_gpa);
fprintf('the bootstraped estimate of the SE of the variance of gpa is %10.5f\n', std( bootstat ) ); 
fprintf('the bootstraped estimate of the bias in the variance of gpa is %10.5f\n', mean( bootstat )-sam_var_gpa );